Math 1303 Review for Test #2 Linear: Equations/Inequalities

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Math 1303
Review for Test #2
Linear: Equations/Inequalities/Systems/Programming
1. Page 11 (17 – 24; 25 – 28) Solve each inequality. Sketch the solution graph on a number line and write
the solution in interval notation.
a. 2(2x + 3) < 6(x – 2) + 10
b. −8 < 3x – 5 < 7
2. See notes and quizzes. Use the “sign chart” method for determining the solution to the inequality. Graph
the solution on a number line and write the solution in interval notation.
a. x2 – 13x + 36 > 0
x 2  7 x  12
< 0
x5
b.
3. See notes and quizzes. Write the equation of each line described below:
a. Tangent to the circle (whose equation is shown below) at the point (−2, −1).
x2 + y2 – 4x – 6y – 19 = 0
4-5. Page 179 (17 – 26); Page 191 (45 – 49); Page 202 (39 – 41) Solve each linear system (use
whichever method your prefer (examples are of each method)
a. Graph:
2 x  3 y  12

 x  2y  6
b. Substitution:
c. Linear combination (addition):
 3x  y  1

 7 x  2 y  1
2 x  4 y  8

3 x  2 y  4
d. Gauss-Jordan (use calculator---show appropriate work):
3 x  5 y  9

2 x  3 y  5
 3x  2 y  8 z  9

 2 x  2 y  z  3
 x  2 y  3z  8

6. Page 180 (57 (ABC), 58 (ABC), 61A, 62A, 63A, 64A, 71); Page 203 (65A, 66A)
a. We are interested in analyzing the sale of cherries each day in a particular town. An analyst arrives
at the following price-demand and price-supply models:
Supply: p = −0.2q + 4
Demand: p = 0.07q + 0.76
p = price (dollars) q = # pounds (1000’s)
How many pounds of cherries can be sold if the price is $2 per pound?
How many pounds of cherries can the supplier provide is the price is $2 per pound?
Find the equilibrium price and quantity.
b. Set up a system of equations and then solve:
Michael Perez has a total of $2,000 on deposit with two savings institutions. One pays interest at the
rate of 6% per year, whereas the other pays interest at the rate of 8% per year. If Michael earned a
total of $144 in interest during a single year, how much does he have on deposit in each account?
7. Page 256 (1 – 10; 33-37) Sketch the graph of the linear inequality: 4x – 5y > 40
8. Page 263 (13 – 22) Sketch the graph of the linear system shown below. Then find all corner points.
Determine whether the solution region is bounded or unbounded.
x > 2
5x + 3y > 30
x – 3y > 0
9.
Page 273 (9 – 16) Solve the linear programming problem:
Maximize P = 4x + 2y
subject to
x+y < 8
2x + y < 10
x > 0
y > 0
10. Page 275 (31A, 32A 33A, 34AB)
Set up a linear programming problem to solve the following. Then use the graphing method to find the
needed value.
National Business Machines manufactures two models of fax machines: A and B. Each model A
costs $100 to make, and each model B costs $150. The profits are $30 for each model A and $40
for each model B fax machine. If the total number of fax machines demanded per month does not
exceed 2500 and the company has earmarked no more than $330,000 per month for manufacturing
costs, how many units of each model should National make each month in order to maximize its
monthly profit? What is the optimal profit?
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